A Comprehensive study of arithmetic circuits and elliptic curves for efficient and scalable zero-knowledge proof systems
In recent years, zero-knowledge proofs have come to play a crucial role in distributed systems where there is no trust between the parties involved. Most popular proof systems are for the NP-complete language of arithmetic circuit satisfiability. Although there have been tremendous efforts in unders...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/689318 |
| Acceso en línea: | http://hdl.handle.net/10803/689318 |
| Access Level: | acceso abierto |
| Palabra clave: | Blockchain Zero-knowledge proof Arithmetic circuit Elliptic curve Cadena de blocs Prova de coneixement zero Circuit aritmètic Corba el·líptica 62 |
| Sumario: | In recent years, zero-knowledge proofs have come to play a crucial role in distributed systems where there is no trust between the parties involved. Most popular proof systems are for the NP-complete language of arithmetic circuit satisfiability. Although there have been tremendous efforts in understanding, developing, and improving zero-knowledge proof systems, not much work has been done towards the study of arithmetic circuits. In this thesis, we contribute to this matter in three different aspects. First, we present circom, a programming language for writing arithmetic circuits that abstracts the complexity of the proof system. Second, we provide a deterministic algorithm for generating twisted Edwards elliptic curves that can be used to prove elliptic-curve cryptography statements in zero knowledge efficiently. Finally, we explore recursive composition of pairing-based proof systems with native circuit arithmetic, delving into the study of cycles of pairing-friendly elliptic curves of prime order. |
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